Abstract
Abstract In this chapter, we present analytical approximate solutions to the values of American barrier options and American lookback strike options. In barrier options, one specifies a barrier. Once the value of the underlying asset reaches the barrier, the “out” barrier option becomes worthless and the “in” barrier option becomes alive. Lookback options are path-dependent options whose payoff depends on the maximum or the minimum realized value of the underlying asset over the life of the option. Our theoretical predictions for the values of these American-style exotic options are in excellent agreement with the results obtained from direct numerical computations.
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